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%I #5 Sep 11 2017 19:50:23
%S 0,1,1,2,5,12,33,90,261,766,2312,7067,21962,68944,218718,699423,
%T 2253303,7304522,23812437,78008885,256688310,847979474,2811399583,
%U 9351303948,31196953900,104359901859,349979094150,1176395410202,3962715659611,13375015304266
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than ten.
%H Alois P. Heinz, <a href="/A292216/b292216.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p b:= proc(n, i, v) option remember; `if`(n=0,
%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p `if`(v=n, 1, add(binomial(a(i)+j-1, j)*
%p b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
%p end:
%p a:= proc(n) option remember; `if`(n<2, n,
%p add(b(n, n+1-j, j), j=2..min(n, 10)))
%p end:
%p seq(a(n), n=0..35);
%Y Column k=10 of A292085.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Sep 11 2017
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